Block #132,797

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 8/25/2013, 3:33:28 AM · Difficulty 9.7907 · 6,694,432 confirmations

TWN

Bi-Twin Chain

Interleaved pairs of primes that differ by 2, forming twin prime pairs at each level.

Block Header

Block Hash

c825a35272f9d5abb378f4648d9e55ee3b3b5739492061e0813bfd2b79d46238

View on Chainz ↗

Height

#132,797

Difficulty

9.790748

Transactions

Size

198 B

Version

Bits

09ca6e76

Nonce

286,867

Timestamp

8/25/2013, 3:33:28 AM

Confirmations

6,694,432

Mined by

⛏️ P2SHAexc4U5CoHjGPXZzEtHuX2ZaZqVzkLuBQ9

Merkle Root

a3a5868b639e4d195bf2a18f232962dbda5428b606573bd06ecd5a5ea8580fb0

Transactions (1)

Coinbasea3a5868b639e4d…cd5a5ea8580fb0

1 in → 1 out10.4200 XPM109 B

Aexc4U5C…VzkLuBQ9

Prime Chain Origin

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) — it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

2.740 × 10⁹¹(92-digit number)

27401147455082899620…01170200403458613759

Discovered Prime Numbers

Lower: 2^k × origin − 1 | Upper: 2^k × origin + 1

These are the actual prime numbers discovered by this block, computed using the verified Primecoin formula. Each number has been independently confirmed to pass the Fermat primality test. Use the FactorDB links to verify any number independently.

Level 0 — Twin Prime Pair (origin ± 1)

origin − 1

2.740 × 10⁹¹(92-digit number)

27401147455082899620…01170200403458613759

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.740 × 10⁹¹(92-digit number)

27401147455082899620…01170200403458613761

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: origin + 1 − origin − 1 = 2 (twin primes ✓)

Level 1 — Twin Prime Pair (2^1 × origin ± 1)

2^1 × origin − 1

5.480 × 10⁹¹(92-digit number)

54802294910165799240…02340400806917227519

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.480 × 10⁹¹(92-digit number)

54802294910165799240…02340400806917227521

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^1 × origin + 1 − 2^1 × origin − 1 = 2 (twin primes ✓)

Level 2 — Twin Prime Pair (2^2 × origin ± 1)

2^2 × origin − 1

1.096 × 10⁹²(93-digit number)

10960458982033159848…04680801613834455039

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.096 × 10⁹²(93-digit number)

10960458982033159848…04680801613834455041

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^2 × origin + 1 − 2^2 × origin − 1 = 2 (twin primes ✓)

Level 3 — Twin Prime Pair (2^3 × origin ± 1)

2^3 × origin − 1

2.192 × 10⁹²(93-digit number)

21920917964066319696…09361603227668910079

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.192 × 10⁹²(93-digit number)

21920917964066319696…09361603227668910081

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^3 × origin + 1 − 2^3 × origin − 1 = 2 (twin primes ✓)

Level 4 — Twin Prime Pair (2^4 × origin ± 1)

2^4 × origin − 1

4.384 × 10⁹²(93-digit number)

43841835928132639392…18723206455337820159

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 9 consecutive prime numbers forming a Bi-Twin Chain. The prime chain origin — the large number shown above — anchors the chain and is divisible by a primorial (the product of small primes), cryptographically tying these prime numbers to this specific block.

★☆☆☆☆

Rarity

CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

How Primecoin's Proof-of-Work Constructs These Primes

Primecoin stores a value called the prime chain origin in each block. The miner found a large integer such that when divided by a primorial (the product of small primes: 2 × 3 × 5 × 7 × …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial — that divisibility is part of the proof.

Prime Chain Origin = First Prime × Primorial (2·3·5·7·11·…)

Source: Primecoin prime.cpp — CheckPrimeProofOfWork()

This is why the origin has many small prime factors — those factors are the primorial divisor. The chain then extends from the first prime using the TWN formula:

TWN: twin pairs (p, p+2) where p = origin/primorial − 1 and p+2 = origin/primorial + 1

Cross-reference on Chainz Explorer

Block #132,797

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